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<ul><li>s[i]=s[i-1]+a[i]</li> <li>s[m]-s[n]=a[n+1]+...+a[m]  m&gt;n</li></ul></li> <li>二维前缀和
<ul><li><code>s[i][j]=s[i-1][j]+s[i][j-1]-s[i-1][j-1]+a[i][j]</code></li></ul></li></ul> <h3 id="leetcode"><a href="#leetcode" class="header-anchor">#</a> LeetCode</h3> <h4 id="_1248-统计「优美子数组」"><a href="#_1248-统计「优美子数组」" class="header-anchor">#</a> <a href="https://leetcode.cn/problems/count-number-of-nice-subarrays/description/" target="_blank" rel="noopener noreferrer">1248. 统计「优美子数组」<span><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15" class="icon outbound"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path> <polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg> <span class="sr-only">(opens new window)</span></span></a></h4> <p>给你一个整数数组 <code>nums</code> 和一个整数 <code>k</code>。如果某个连续子数组中恰好有 <code>k</code> 个奇数数字，我们就认为这个子数组是「<strong>优美子数组</strong>」。</p> <p>请返回这个数组中 <strong>「优美子数组」</strong> 的数目。</p> <p><strong>示例 1：</strong></p> <div class="language- line-numbers-mode"><pre class="language-text"><code>输入：num
s = [1,1,2,1,1], k = 3
输出：2
解释：包含 3 个奇数的子数组是 [1,1,2,1] 和 [1,2,1,1] 。
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br></div></div><p><strong>示例 2：</strong></p> <div class="language- line-numbers-mode"><pre class="language-text"><code>输入：nums = [2,4,6], k = 1
输出：0
解释：数列中不包含任何奇数，所以不存在优美子数组。
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br></div></div><p><strong>示例 3：</strong></p> <div class="language- line-numbers-mode"><pre class="language-text"><code>输入：nums = [2,2,2,1,2,2,1,2,2,2], k = 2
输出：16
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br></div></div><p><strong>提示：</strong></p> <ul><li><code>1 &lt;= nums.length &lt;= 50000</code></li> <li><code>1 &lt;= nums[i] &lt;= 10^5</code></li> <li><code>1 &lt;= k &lt;= nums.length</code></li></ul> <h5 id="完整代码"><a href="#完整代码" class="header-anchor">#</a> 完整代码</h5> <div class="language-js line-numbers-mode"><pre class="language-js"><code><span class="token comment">/**
 * @param {number[]} nums
 * @param {number} k
 * @return {number}
 */</span>
<span class="token keyword">var</span> <span class="token function-variable function">numberOfSubarrays</span> <span class="token operator">=</span> <span class="token keyword">function</span><span class="token punctuation">(</span><span class="token parameter">nums<span class="token punctuation">,</span> k</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>

    <span class="token comment">// 解题思路</span>

    <span class="token comment">// 连续子数组恰有k个奇数数字</span>
    <span class="token comment">// 我们把偶数置为0，奇数置为1</span>
    <span class="token comment">// 问题转换为连续子数组的和为k</span>

    <span class="token comment">// 转换为前缀和 即s[i]-s[j]=k</span>
    <span class="token comment">// 即s[j]=s[i]-k  ==&gt; s[j]&gt;=0   ==&gt;s[i]-k&gt;=0</span>

    <span class="token comment">// s[i]-k 其实是前缀和s[j]   那么这样的s[j]有多少个呢 即统计s[j] 的count</span>

    <span class="token comment">// 转换数组并计算前缀和</span>

    <span class="token comment">// 定义一个count数组，通过s[j]的个数</span>
    <span class="token keyword">let</span> count<span class="token operator">=</span><span class="token keyword">new</span> <span class="token class-name">Array</span><span class="token punctuation">(</span>nums<span class="token punctuation">.</span>length<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">.</span><span class="token function">fill</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">)</span>
    count<span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span><span class="token operator">=</span><span class="token number">1</span>
    <span class="token keyword">let</span> s<span class="token operator">=</span><span class="token keyword">new</span> <span class="token class-name">Array</span><span class="token punctuation">(</span>nums<span class="token punctuation">.</span>length<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">.</span><span class="token function">fill</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">)</span>
    <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">let</span> i<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span>i<span class="token operator">&lt;</span>nums<span class="token punctuation">.</span>length<span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
        nums<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token operator">=</span>nums<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token operator">%</span><span class="token number">2</span>
        s<span class="token punctuation">[</span>i<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token operator">=</span>s<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token operator">+</span>nums<span class="token punctuation">[</span>i<span class="token punctuation">]</span>
        count<span class="token punctuation">[</span>s<span class="token punctuation">[</span>i<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">]</span><span class="token operator">++</span>
    <span class="token punctuation">}</span>

    console<span class="token punctuation">.</span><span class="token function">log</span><span class="token punctuation">(</span>s<span class="token punctuation">)</span>

    <span class="token keyword">let</span> res<span class="token operator">=</span><span class="token number">0</span>
    <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">let</span> i<span class="token operator">=</span><span class="token number">1</span><span class="token punctuation">;</span>i<span class="token operator">&lt;</span>nums<span class="token punctuation">.</span>length<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span>s<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token operator">-</span>k<span class="token operator">&gt;=</span><span class="token number">0</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
            res<span class="token operator">+=</span>count<span class="token punctuation">[</span>s<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token operator">-</span>k<span class="token punctuation">]</span>
        <span class="token punctuation">}</span>
    <span class="token punctuation">}</span>

    <span class="token keyword">return</span> res

<span class="token punctuation">}</span><span class="token punctuation">;</span>
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br><span class="line-number">9</span><br><span class="line-number">10</span><br><span class="line-number">11</span><br><span class="line-number">12</span><br><span class="line-number">13</span><br><span class="line-number">14</span><br><span class="line-number">15</span><br><span class="line-number">16</span><br><span class="line-number">17</span><br><span class="line-number">18</span><br><span class="line-number">19</span><br><span class="line-number">20</span><br><span class="line-number">21</span><br><span class="line-number">22</span><br><span class="line-number">23</span><br><span class="line-number">24</span><br><span class="line-number">25</span><br><span class="line-number">26</span><br><span class="line-number">27</span><br><span class="line-number">28</span><br><span class="line-number">29</span><br><span class="line-number">30</span><br><span class="line-number">31</span><br><span class="line-number">32</span><br><span class="line-number">33</span><br><span class="line-number">34</span><br><span class="line-number">35</span><br><span class="line-number">36</span><br><span class="line-number">37</span><br><span class="line-number">38</span><br><span class="line-number">39</span><br><span class="line-number">40</span><br><span class="line-number">41</span><br><span class="line-number">42</span><br></div></div><h4 id="_304-二维区域和检索-矩阵不可变-模板题"><a href="#_304-二维区域和检索-矩阵不可变-模板题" class="header-anchor">#</a> <a href="https://leetcode.cn/problems/range-sum-query-2d-immutable/description/" target="_blank" rel="noopener noreferrer">304. 二维区域和检索 - 矩阵不可变（模板题）<span><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15" class="icon outbound"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path> <polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg> <span class="sr-only">(opens new window)</span></span></a></h4> <p>给定一个二维矩阵 <code>matrix</code>，以下类型的多个请求：</p> <ul><li>计算其子矩形范围内元素的总和，该子矩阵的 <strong>左上角</strong> 为 <code>(row1, col1)</code> ，<strong>右下角</strong> 为 <code>(row2, col2)</code> 。</li></ul> <p>实现 <code>NumMatrix</code> 类：</p> <ul><li><code>NumMatrix(int[][] matrix)</code> 给定整数矩阵 <code>matrix</code> 进行初始化</li> <li><code>int sumRegion(int row1, int col1, int row2, int col2)</code> 返回 <strong>左上角</strong> <code>(row1, col1)</code> 、<strong>右下角</strong> <code>(row2, col2)</code> 所描述的子矩阵的元素 <strong>总和</strong> 。</li></ul> <p><strong>示例 1：</strong></p> <p><img src="https://pic.leetcode-cn.com/1626332422-wUpUHT-image.png" alt="img"></p> <div class="language- line-numbers-mode"><pre class="language-text"><code>输入: 
[&quot;NumMatrix&quot;,&quot;sumRegion&quot;,&quot;sumRegion&quot;,&quot;sumRegion&quot;]
[[[[3,0,1,4,2],[5,6,3,2,1],[1,2,0,1,5],[4,1,0,1,7],[1,0,3,0,5]]],[2,1,4,3],[1,1,2,2],[1,2,2,4]]
输出: 
[null, 8, 11, 12]

解释:
NumMatrix numMatrix = new NumMatrix([[3,0,1,4,2],[5,6,3,2,1],[1,2,0,1,5],[4,1,0,1,7],[1,0,3,0,5]]);
numMatrix.sumRegion(2, 1, 4, 3); // return 8 (红色矩形框的元素总和)
numMatrix.sumRegion(1, 1, 2, 2); // return 11 (绿色矩形框的元素总和)
numMatrix.sumRegion(1, 2, 2, 4); // return 12 (蓝色矩形框的元素总和)
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br><span class="line-number">9</span><br><span class="line-number">10</span><br><span class="line-number">11</span><br></div></div><p><strong>提示：</strong></p> <ul><li><code>m == matrix.length</code></li> <li><code>n == matrix[i].length</code></li> <li><code>1 &lt;= m, n &lt;= 200</code></li> <li><code>-105 &lt;= matrix[i][j] &lt;= 105</code></li> <li><code>0 &lt;= row1 &lt;= row2 &lt; m</code></li> <li><code>0 &lt;= col1 &lt;= col2 &lt; n</code></li> <li>最多调用 <code>104</code> 次 <code>sumRegion</code> 方法</li></ul> <h5 id="解题思路"><a href="#解题思路" class="header-anchor">#</a> 解题思路</h5> <div class="language-shell line-numbers-mode"><pre class="language-shell"><code><span class="token number">1</span>. 二维前缀和
<span class="token number">2</span>. 面积计算，计算阴影面积一样，
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br></div></div><h5 id="完整代码-2"><a href="#完整代码-2" class="header-anchor">#</a> 完整代码</h5> <div class="language-js line-numbers-mode"><pre class="language-js"><code><span class="token comment">/**
 * @param {number[][]} matrix
 */</span>
<span class="token keyword">var</span> <span class="token function-variable function">NumMatrix</span> <span class="token operator">=</span> <span class="token keyword">function</span><span class="token punctuation">(</span><span class="token parameter">matrix</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>

    <span class="token comment">// 生成二维前缀和矩阵</span>
    <span class="token keyword">let</span> m<span class="token operator">=</span>matrix<span class="token punctuation">.</span>length
    <span class="token keyword">let</span> n<span class="token operator">=</span>matrix<span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span><span class="token punctuation">.</span>length
    <span class="token comment">// this.sums=new Array(m+1).fill(new Array(n+1).fill(0))</span>

    <span class="token keyword">this</span><span class="token punctuation">.</span>sums <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">Array</span><span class="token punctuation">(</span>m <span class="token operator">+</span> <span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">.</span><span class="token function">fill</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">)</span><span class="token punctuation">.</span><span class="token function">map</span><span class="token punctuation">(</span><span class="token punctuation">(</span><span class="token punctuation">)</span> <span class="token operator">=&gt;</span> <span class="token keyword">new</span> <span class="token class-name">Array</span><span class="token punctuation">(</span>n <span class="token operator">+</span> <span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">.</span><span class="token function">fill</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>

    <span class="token comment">// console.log(this.sums)</span>
    <span class="token comment">// console.log(matrix)</span>
    
    <span class="token comment">// 生成二维前缀和</span>
    <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">let</span> i<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span>i<span class="token operator">&lt;</span>m<span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
        <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">let</span> j<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span>j<span class="token operator">&lt;</span>n<span class="token punctuation">;</span>j<span class="token operator">++</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
            <span class="token keyword">this</span><span class="token punctuation">.</span>sums<span class="token punctuation">[</span>i<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">[</span>j<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token operator">=</span><span class="token keyword">this</span><span class="token punctuation">.</span>sums<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">[</span>j<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token operator">+</span><span class="token keyword">this</span><span class="token punctuation">.</span>sums<span class="token punctuation">[</span>i<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">[</span>j<span class="token punctuation">]</span><span class="token operator">-</span><span class="token keyword">this</span><span class="token punctuation">.</span>sums<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">[</span>j<span class="token punctuation">]</span><span class="token operator">+</span>matrix<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">[</span>j<span class="token punctuation">]</span>
        <span class="token punctuation">}</span>
    <span class="token punctuation">}</span>

    <span class="token comment">// console.log(this.sums[0][1])</span>

<span class="token punctuation">}</span><span class="token punctuation">;</span>

<span class="token comment">/** 
 * @param {number} row1 
 * @param {number} col1 
 * @param {number} row2 
 * @param {number} col2
 * @return {number}
 */</span>
<span class="token class-name">NumMatrix</span><span class="token punctuation">.</span>prototype<span class="token punctuation">.</span><span class="token function-variable function">sumRegion</span> <span class="token operator">=</span> <span class="token keyword">function</span><span class="token punctuation">(</span><span class="token parameter">row1<span class="token punctuation">,</span> col1<span class="token punctuation">,</span> row2<span class="token punctuation">,</span> col2</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
    <span class="token comment">// console.log(this.sums)</span>

    <span class="token comment">// 计算阴影面积</span>
    <span class="token keyword">return</span> <span class="token keyword">this</span><span class="token punctuation">.</span>sums<span class="token punctuation">[</span>row2<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">[</span>col2<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token operator">-</span><span class="token keyword">this</span><span class="token punctuation">.</span>sums<span class="token punctuation">[</span>row1<span class="token punctuation">]</span><span class="token punctuation">[</span>col2<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token operator">-</span><span class="token keyword">this</span><span class="token punctuation">.</span>sums<span class="token punctuation">[</span>row2<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">[</span>col1<span class="token punctuation">]</span><span class="token operator">+</span><span class="token keyword">this</span><span class="token punctuation">.</span>sums<span class="token punctuation">[</span>row1<span class="token punctuation">]</span><span class="token punctuation">[</span>col1<span class="token punctuation">]</span>
<span class="token punctuation">}</span><span class="token punctuation">;</span>

<span class="token comment">/**
 * Your NumMatrix object will be instantiated and called as such:
 * var obj = new NumMatrix(matrix)
 * var param_1 = obj.sumRegion(row1,col1,row2,col2)
 */</span>
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br><span class="line-number">9</span><br><span class="line-number">10</span><br><span class="line-number">11</span><br><span class="line-number">12</span><br><span class="line-number">13</span><br><span class="line-number">14</span><br><span class="line-number">15</span><br><span class="line-number">16</span><br><span class="line-number">17</span><br><span class="line-number">18</span><br><span class="line-number">19</span><br><span class="line-number">20</span><br><span class="line-number">21</span><br><span class="line-number">22</span><br><span class="line-number">23</span><br><span class="line-number">24</span><br><span class="line-number">25</span><br><span class="line-number">26</span><br><span class="line-number">27</span><br><span class="line-number">28</span><br><span class="line-number">29</span><br><span class="line-number">30</span><br><span class="line-number">31</span><br><span class="line-number">32</span><br><span class="line-number">33</span><br><span class="line-number">34</span><br><span class="line-number">35</span><br><span class="line-number">36</span><br><span class="line-number">37</span><br><span class="line-number">38</span><br><span class="line-number">39</span><br><span class="line-number">40</span><br><span class="line-number">41</span><br><span class="line-number">42</span><br><span class="line-number">43</span><br><span class="line-number">44</span><br><span class="line-number">45</span><br></div></div><h2 id="_2-差分"><a href="#_2-差分" class="header-anchor">#</a> 2.差分</h2> <ul><li><p>原数组A</p> <ul><li><code>[1,2,1,3,2]</code></li></ul></li> <li><p>差分数组B，b[1]=a[1] , b[i]=a[i]-a[i-1]</p> <ul><li><code>[1,1,-1,2,-1]</code></li></ul></li> <li><p>性质</p> <ul><li>差分数组B的前缀和数组为原数组A</li> <li>将原数组m-n之间的元素+d，对应的差分数组B，B[m]+d，B[n+1]+d</li></ul></li></ul> <h3 id="leetcode-2"><a href="#leetcode-2" class="header-anchor">#</a> LeetCode</h3> <h4 id="_1109-航班预订统计"><a href="#_1109-航班预订统计" class="header-anchor">#</a> 1109. 航班预订统计</h4> <p>这里有 <code>n</code> 个航班，它们分别从 <code>1</code> 到 <code>n</code> 进行编号。</p> <p>有一份航班预订表 <code>bookings</code> ，表中第 <code>i</code> 条预订记录 <code>bookings[i] = [firsti, lasti, seatsi]</code> 意味着在从 <code>firsti</code> 到 <code>lasti</code> （<strong>包含</strong> <code>firsti</code> 和 <code>lasti</code> ）的 <strong>每个航班</strong> 上预订了 <code>seatsi</code> 个座位。</p> <p>请你返回一个长度为 <code>n</code> 的数组 <code>answer</code>，里面的元素是每个航班预定的座位总数。</p> <p><strong>示例 1：</strong></p> <div class="language- line-numbers-mode"><pre class="language-text"><code>输入：bookings = [[1,2,10],[2,3,20],[2,5,25]], n = 5
输出：[10,55,45,25,25]
解释：
航班编号        1   2   3   4   5
预订记录 1 ：   10  10
预订记录 2 ：       20  20
预订记录 3 ：       25  25  25  25
总座位数：      10  55  45  25  25
因此，answer = [10,55,45,25,25]
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br><span class="line-number">9</span><br></div></div><p><strong>示例 2：</strong></p> <div class="language- line-numbers-mode"><pre class="language-text"><code>输入：bookings = [[1,2,10],[2,2,15]], n = 2
输出：[10,25]
解释：
航班编号        1   2
预订记录 1 ：   10  10
预订记录 2 ：       15
总座位数：      10  25
因此，answer = [10,25]
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br></div></div><p><strong>提示：</strong></p> <ul><li><code>1 &lt;= n &lt;= 2 * 104</code></li> <li><code>1 &lt;= bookings.length &lt;= 2 * 104</code></li> <li><code>bookings[i].length == 3</code></li> <li><code>1 &lt;= firsti &lt;= lasti &lt;= n</code></li> <li><code>1 &lt;= seatsi &lt;= 104</code></li></ul> <h5 id="解题思路-2"><a href="#解题思路-2" class="header-anchor">#</a> 解题思路</h5> <div class="language-shell line-numbers-mode"><pre class="language-shell"><code><span class="token number">1</span>. 如果使用朴素算法，则需要遍历k*n次 k为预定记录数，n为每条记录预定的航班（超时）
<span class="token number">2</span>. 使用差分，因为我们发现每个预定记录k，预定的航班是连续的，且票数相同，其实我们只需要算首尾就行了
   时间复杂度2*k
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br></div></div><h5 id="完整代码-3"><a href="#完整代码-3" class="header-anchor">#</a> 完整代码</h5> <div class="language-js line-numbers-mode"><pre class="language-js"><code><span class="token comment">/**
 * @param {number[][]} bookings
 * @param {number} n
 * @return {number[]}
 */</span>
<span class="token keyword">var</span> <span class="token function-variable function">corpFlightBookings</span> <span class="token operator">=</span> <span class="token keyword">function</span><span class="token punctuation">(</span><span class="token parameter">bookings<span class="token punctuation">,</span> n</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>

    <span class="token comment">// 使用差分数组</span>

    <span class="token comment">// 原数组 都为0，差分数组也是都为0</span>
    <span class="token keyword">let</span> b<span class="token operator">=</span><span class="token keyword">new</span> <span class="token class-name">Array</span><span class="token punctuation">(</span>n<span class="token operator">+</span><span class="token number">2</span><span class="token punctuation">)</span><span class="token punctuation">.</span><span class="token function">fill</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">)</span>

    <span class="token comment">// m到n加上一个数，差分数组b[m]+数 b[n+1]-数</span>

    bookings<span class="token punctuation">.</span><span class="token function">forEach</span><span class="token punctuation">(</span><span class="token parameter">item</span><span class="token operator">=&gt;</span><span class="token punctuation">{</span>
        b<span class="token punctuation">[</span>item<span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span><span class="token punctuation">]</span><span class="token operator">+=</span>item<span class="token punctuation">[</span><span class="token number">2</span><span class="token punctuation">]</span>
        b<span class="token punctuation">[</span>item<span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token operator">-=</span>item<span class="token punctuation">[</span><span class="token number">2</span><span class="token punctuation">]</span>
    <span class="token punctuation">}</span><span class="token punctuation">)</span>

    <span class="token comment">// 得到b的前缀和数组，即可以得到原数组</span>

    <span class="token keyword">let</span> s<span class="token operator">=</span><span class="token keyword">new</span> <span class="token class-name">Array</span><span class="token punctuation">(</span>n<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">)</span>
    s<span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span><span class="token operator">=</span><span class="token number">0</span>
    <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">let</span> i<span class="token operator">=</span><span class="token number">1</span><span class="token punctuation">;</span>i<span class="token operator">&lt;</span>b<span class="token punctuation">.</span>length<span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
        s<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token operator">=</span>s<span class="token punctuation">[</span>i<span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token operator">+</span>b<span class="token punctuation">[</span>i<span class="token punctuation">]</span>
    <span class="token punctuation">}</span>

    <span class="token keyword">return</span> s<span class="token punctuation">.</span><span class="token function">slice</span><span class="token punctuation">(</span><span class="token number">1</span><span class="token punctuation">)</span>


<span class="token punctuation">}</span><span class="token punctuation">;</span>
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br><span class="line-number">9</span><br><span class="line-number">10</span><br><span class="line-number">11</span><br><span class="line-number">12</span><br><span class="line-number">13</span><br><span class="line-number">14</span><br><span class="line-number">15</span><br><span class="line-number">16</span><br><span class="line-number">17</span><br><span class="line-number">18</span><br><span class="line-number">19</span><br><span class="line-number">20</span><br><span class="line-number">21</span><br><span class="line-number">22</span><br><span class="line-number">23</span><br><span class="line-number">24</span><br><span class="line-number">25</span><br><span class="line-number">26</span><br><span class="line-number">27</span><br><span class="line-number">28</span><br><span class="line-number">29</span><br><span class="line-number">30</span><br><span class="line-number">31</span><br></div></div><h4 id="_53-最大子数组和"><a href="#_53-最大子数组和" class="header-anchor">#</a> 53. 最大子数组和</h4> <p>给你一个整数数组 <code>nums</code> ，请你找出一个具有最大和的连续子数组（子数组最少包含一个元素），返回其最大和。</p> <p><strong>子数组</strong> 是数组中的一个连续部分。</p> <p><strong>示例 1：</strong></p> <div class="language- line-numbers-mode"><pre class="language-text"><code>输入：nums = [-2,1,-3,4,-1,2,1,-5,4]
输出：6
解释：连续子数组 [4,-1,2,1] 的和最大，为 6 。
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br></div></div><p><strong>示例 2：</strong></p> <div class="language- line-numbers-mode"><pre class="language-text"><code>输入：nums = [1]
输出：1
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br></div></div><p><strong>示例 3：</strong></p> <div class="language- line-numbers-mode"><pre class="language-text"><code>输入：nums = [5,4,-1,7,8]
输出：23
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br></div></div><p><strong>提示：</strong></p> <ul><li><code>1 &lt;= nums.length &lt;= 105</code></li> <li><code>-104 &lt;= nums[i] &lt;= 104</code></li></ul> <p>**进阶：**如果你已经实现复杂度为 <code>O(n)</code> 的解法，尝试使用更为精妙的 <strong>分治法</strong> 求解。</p> <h5 id="完整代码-4"><a href="#完整代码-4" class="header-anchor">#</a> 完整代码</h5> <div class="language-js line-numbers-mode"><pre class="language-js"><code><span class="token comment">/**
 * @param {number[]} nums
 * @return {number}
 */</span>
<span class="token keyword">var</span> <span class="token function-variable function">maxSubArray</span> <span class="token operator">=</span> <span class="token keyword">function</span><span class="token punctuation">(</span><span class="token parameter">nums</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>

    <span class="token comment">// 解题思路</span>

    <span class="token comment">// 即求 a[m]+a[m+1]+....+a[n] 为最大</span>

    <span class="token comment">// 一般遇到这么的，转换为s[n]-s[m-1]</span>

    <span class="token comment">// 所以我们先求出前缀和数组</span>
    <span class="token keyword">let</span> s<span class="token operator">=</span><span class="token keyword">new</span> <span class="token class-name">Array</span><span class="token punctuation">(</span>nums<span class="token punctuation">.</span>length<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">.</span><span class="token function">fill</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">)</span>
    s<span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span><span class="token operator">=</span><span class="token number">0</span>
    <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">let</span> i<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span>i<span class="token operator">&lt;</span>nums<span class="token punctuation">.</span>length<span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
        s<span class="token punctuation">[</span>i<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token operator">=</span>s<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token operator">+</span>nums<span class="token punctuation">[</span>i<span class="token punctuation">]</span>
    <span class="token punctuation">}</span>

    <span class="token comment">// 问题已经转换为s[n]-s[m] 为最大</span>
    <span class="token comment">// 即在n不变的情况下，寻找s[m]为最小 且m&lt;n ,即前缀和s[m]最小</span>
    <span class="token comment">// 先求前缀最小值，sMin(5) 前5个元素最小和</span>

    <span class="token keyword">let</span> sMin<span class="token operator">=</span><span class="token keyword">new</span> <span class="token class-name">Array</span><span class="token punctuation">(</span>nums<span class="token punctuation">.</span>length<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">.</span><span class="token function">fill</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">)</span>
    sMin<span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span><span class="token operator">=</span><span class="token number">0</span>
    <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">let</span> i<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span>i<span class="token operator">&lt;</span>nums<span class="token punctuation">.</span>length<span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
        sMin<span class="token punctuation">[</span>i<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token operator">=</span>Math<span class="token punctuation">.</span><span class="token function">min</span><span class="token punctuation">(</span>sMin<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">,</span>s<span class="token punctuation">[</span>i<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">)</span>
    <span class="token punctuation">}</span>


    <span class="token comment">// 回归问题，求满足s[i]-s[j] 为 最大的s[j],即s[j]最小，且j&lt;i</span>

    <span class="token comment">// 而前缀最小和sMin[j] 即为s[j] 最小</span>

    <span class="token keyword">let</span> res<span class="token operator">=</span><span class="token operator">-</span><span class="token number">Infinity</span>
    <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">let</span> i<span class="token operator">=</span><span class="token number">1</span><span class="token punctuation">;</span>i<span class="token operator">&lt;</span>nums<span class="token punctuation">.</span>length<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
        res<span class="token operator">=</span>Math<span class="token punctuation">.</span><span class="token function">max</span><span class="token punctuation">(</span>res<span class="token punctuation">,</span>s<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token operator">-</span>sMin<span class="token punctuation">[</span>i<span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">)</span>
    <span class="token punctuation">}</span>

    <span class="token keyword">return</span> res
<span class="token punctuation">}</span><span class="token punctuation">;</span>
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br><span class="line-number">9</span><br><span class="line-number">10</span><br><span class="line-number">11</span><br><span class="line-number">12</span><br><span class="line-number">13</span><br><span class="line-number">14</span><br><span class="line-number">15</span><br><span class="line-number">16</span><br><span class="line-number">17</span><br><span class="line-number">18</span><br><span class="line-number">19</span><br><span class="line-number">20</span><br><span class="line-number">21</span><br><span class="line-number">22</span><br><span class="line-number">23</span><br><span class="line-number">24</span><br><span class="line-number">25</span><br><span class="line-number">26</span><br><span class="line-number">27</span><br><span class="line-number">28</span><br><span class="line-number">29</span><br><span class="line-number">30</span><br><span class="line-number">31</span><br><span class="line-number">32</span><br><span class="line-number">33</span><br><span class="line-number">34</span><br><span class="line-number">35</span><br><span class="line-number">36</span><br><span class="line-number">37</span><br><span class="line-number">38</span><br><span class="line-number">39</span><br><span class="line-number">40</span><br><span class="line-number">41</span><br></div></div></div></div>  <div class="page-edit"><div class="edit-link"><a href="https://github.com/linxin1123/vuepress-blog/edit/master/docs/07.算法/41.算法训练营/04.前缀和-差分-双指针（上）-cnblog.md" target="_blank" rel="noopener noreferrer">编辑</a> <span><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15" class="icon outbound"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path> <polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg> <span class="sr-only">(opens new window)</span></span></div> <!----> <div class="last-updated"><span class="prefix">上次更新:</span> <span class="time">2023/02/17, 11:29:32</span></div></div> <div class="page-nav-wapper"><div class="page-nav-centre-wrap"><a href="/pages/1848ee/" class="page-nav-centre page-nav-centre-prev"><div class="tooltip">哈希表-集合-映射-cnblog</div></a> <a href="/pages/9b8692/" class="page-nav-centre page-nav-centre-next"><div class="tooltip">前缀和-差分-双指针（下）-cnblog</div></a></div> <div class="page-nav"><p class="inner"><span class="prev">
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